Optimal Tax Progressivity: An Analytical Framework Jonathan Heathcote Federal Reserve Bank of Minneapolis Kjetil Storesletten Oslo University Gianluca Violante New York University Midwest Macro Meetings, Fall 2015 Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Motivation Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
How progressive should labor income taxation be? Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
How progressive should labor income taxation be? • Argument in favor of progressivity: missing markets ◮ Social insurance of privately-uninsurable lifecycle shocks ◮ Redistribution with respect to unequal initial conditions Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
How progressive should labor income taxation be? • Argument in favor of progressivity: missing markets ◮ Social insurance of privately-uninsurable lifecycle shocks ◮ Redistribution with respect to unequal initial conditions • Argument I against progressivity: distortions ◮ Labor supply ◮ Human capital investment Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
How progressive should labor income taxation be? • Argument in favor of progressivity: missing markets ◮ Social insurance of privately-uninsurable lifecycle shocks ◮ Redistribution with respect to unequal initial conditions • Argument I against progressivity: distortions ◮ Labor supply ◮ Human capital investment • Argument II against progressivity: externality ◮ Financing of public good provision Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Overview of the approach • Model ingredients: 1. partial insurance against labor-income risk [ex-post heter.] 2. differential diligence & (learning) ability [ex-ante heter.] Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Overview of the approach • Model ingredients: 1. partial insurance against labor-income risk [ex-post heter.] 2. differential diligence & (learning) ability [ex-ante heter.] 3. flexible labor supply 4. endogenous skill investment + multiple-skill technology Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Overview of the approach • Model ingredients: 1. partial insurance against labor-income risk [ex-post heter.] 2. differential diligence & (learning) ability [ex-ante heter.] 3. flexible labor supply 4. endogenous skill investment + multiple-skill technology 5. government expenditures valued by households Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Overview of the approach • Model ingredients: 1. partial insurance against labor-income risk [ex-post heter.] 2. differential diligence & (learning) ability [ex-ante heter.] 3. flexible labor supply 4. endogenous skill investment + multiple-skill technology 5. government expenditures valued by households • Ramsey approach: mkt structure & tax instruments taken as given Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Overview of the approach • Model ingredients: 1. partial insurance against labor-income risk [ex-post heter.] 2. differential diligence & (learning) ability [ex-ante heter.] 3. flexible labor supply 4. endogenous skill investment + multiple-skill technology 5. government expenditures valued by households • Ramsey approach: mkt structure & tax instruments taken as given → closed-form Social Welfare Function Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
T AX /T RANSFER F UNCTION Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
The tax/transfer function y − T ( y ) = λy 1 − τ • The parameter τ measures the degree of progressivity: ◮ τ = 1 : full redistribution → T ( y ) = y − λ T ′ ( y ) > T ( y ) ◮ 0 < τ < 1 : progressivity → y T ′ ( y ) = T ( y ) ◮ τ = 0 : no redistribution → = 1 − λ y T ′ ( y ) < T ( y ) ◮ τ < 0 : → regressivity y • Break-even income level: y 0 = λ 1 τ Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
The tax/transfer function y − T ( y ) = λy 1 − τ • The parameter τ measures the degree of progressivity: ◮ τ = 1 : full redistribution → T ( y ) = y − λ T ′ ( y ) > T ( y ) ◮ 0 < τ < 1 : progressivity → y T ′ ( y ) = T ( y ) ◮ τ = 0 : no redistribution → = 1 − λ y T ′ ( y ) < T ( y ) ◮ τ < 0 : → regressivity y • Break-even income level: y 0 = λ 1 τ Restrictions: (i) no lump-sum transfer & (ii) T ′ ( y ) monotone Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Measurement of τ US • PSID 2000-06, age of head of hh 25-60, N = 12 , 943 • Pre gov. income: income minus deductions (medical expenses, state taxes, mortgage interest and charitable contributions) • Post-gov income: ... minus taxes (TAXSIM) plus transfers Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Measurement of τ US • PSID 2000-06, age of head of hh 25-60, N = 12 , 943 • Pre gov. income: income minus deductions (medical expenses, state taxes, mortgage interest and charitable contributions) • Post-gov income: ... minus taxes (TAXSIM) plus transfers 13 0.5 12.5 Log of Disposable Income 0.4 12 0.3 11.5 Tax Rates 0.2 11 10.5 0.1 Marginal Tax Rate 10 Average Tax Rate 0 τ US = 0.161 9.5 -0.1 9 -0.2 8.5 -0.3 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 0 1 2 3 4 5 Log of Pre−government Income × 10 5 Pre-government Income Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
M ODEL Heathcote -Storesletten-Violante, ”Optimal Tax Progressivity”
Demographics and preferences • Perpetual youth demographics with constant survival probability δ • Preferences over consumption ( c ) , hours ( h ) , publicly -provided goods ( G ) , and skill-investment ( s ) effort: ∞ � ( βδ ) t u i ( c it , h it , G ) U i = − v i ( s i ) + E 0 t =0 Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Demographics and preferences • Perpetual youth demographics with constant survival probability δ • Preferences over consumption ( c ) , hours ( h ) , publicly -provided goods ( G ) , and skill-investment ( s ) effort: ∞ � ( βδ ) t u i ( c it , h it , G ) U i = − v i ( s i ) + E 0 t =0 ( κ i ) 1 /ψ · s 1+1 /ψ 1 i v i ( s i ) = 1 + 1 /ψ ∼ κ i Exp (1) log c it − exp( ϕ i ) h 1+ σ it u i ( c it , h it , G ) = 1 + σ + χ log G � v ϕ � ∼ N ϕ i ⊥ κ i ϕ i 2 , v ϕ , Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Technology • Aggregate effective hours by skill type: � 1 N ( s ) = I { s i = s } z i h i di 0 • Output is a CES aggregator over continuum of skill types: �� ∞ � θ θ − 1 θ − 1 Y = N ( s ) ds , θ ∈ (1 , ∞ ) θ 0 ◮ Determination of skill price: p ( s ) = MPN ( s ) • Aggregate resource constraint: � 1 Y = c i di + G 0 Heathcote -Storesletten-Violante, ”Optimal Tax Progressivity”
Individual efficiency units of labor log z it = α it + ε it � � • α it = α i,t − 1 + ω it − v ω with ω it ∼ N 2 , v ω [permanent] + � � • ε it − v ε ε it ∼ N 2 , v ε i.i.d. over time with [transitory] • ω it ⊥ ε it cross -sectionally and longitudinally Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Individual efficiency units of labor log z it = α it + ε it � � • α it = α i,t − 1 + ω it − v ω with ω it ∼ N 2 , v ω [permanent] + � � • ε it − v ε ε it ∼ N 2 , v ε i.i.d. over time with [transitory] • ω it ⊥ ε it cross -sectionally and longitudinally • Pre-government earnings: y it = p ( s i ) × exp( α it + ε it ) × h it ���� ���� � �� � hours skill price efficiency determined by skill, fortune, and diligence Heathcote-Storesletten-Violante, ”Optimal Tax Progressivity”
Government • Government budget constraint (no government debt): � 1 � � y i − λy 1 − τ G = di i 0 • Government chooses ( G, τ ) , and λ balances the budget residually • Without loss of generality, we let the government choose: g ≡ G Y Heathcote -Storesletten-Violante, ”Optimal Tax Progressivity”
Market structure • Final good (numeraire) market and labor markets are competitive • Perfect annuity markets against survival risk Heathcote -Storesletten-Violante, ”Optimal Tax Progressivity”
Market structure • Final good (numeraire) market and labor markets are competitive • Perfect annuity markets against survival risk • Full set of insurance claims against ε shocks • No market to insure ω shock [microfoundation with bond] Heathcote -Storesletten-Violante, ”Optimal Tax Progressivity”
Market structure • Final good (numeraire) market and labor markets are competitive • Perfect annuity markets against survival risk • Full set of insurance claims against ε shocks • No market to insure ω shock [microfoundation with bond] � v ε > 0 , v ω > 0 → partial insurance economy � v ω = 0 → full insurance economy � v ω = v ε = v ϕ = 0 & θ = ∞ → RA economy Heathcote -Storesletten-Violante, ”Optimal Tax Progressivity”
Special case: representative agent economy log C − H 1+ σ max U = 1 + σ + χ log gY C,H s.t. λY 1 − τ C = Y = H C + G = Y Heathcote -Storesletten-Violante, ”Optimal Tax Progressivity”
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